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The "why" in those situations can be replaced by "how do we know".
a) We know that if there is an unbalanced force there must be an
acceleration. Given the force we can calculate the acceleration
b) We also know that if there is an acceleration, there must be an
unbalanced force. Given the acceleration we can calculate the force.
Let's be clear: There can be a cause for the knowing, even though
there is not a cause for the acceleration. In some situations (e.g.
the diver) know the force in advance and calculate the acceleration. In other situations (e.g. a centrifuge) you know the acceleration in
advance and calculate the force.
But I know I do say things like: "An unbalanced force causes an
object to accelerate."
I used to say things like that, but I've pretty much trained myself
to not do so anymore. Instead I might say an unbalanced force is
/associated with/ an acceleration. The point is that association
is symmetric, unlike causation which is asymmetric. F=ma is an
equality, and equality is reflective, symmetric, and transitive.
I might also say that given an unbalanced force, we know the object
will accelerate. I might even say that because there is an unbalanced
force, we know the object will accelerate. (There is a cause for the
knowing, even though there is not a cause for the acceleration.)
Sometimes I say "because" when I shouldn't, but I treat this as a
mistake just like any other mistake, and I edit it out if I can.